Sorry to complicate matters, but a single musical tone from a mechanical instrument or from an electronic instrument imitating a mechanical instrument is not a single frequency but rather a combination of frequencies beginning with a fundamental (harmonic) and then a complete harmonic series at octaves, octave fifths, octave thirds (sixths) and so forth. A further complication is that the harmonic series itself often is not precisely harmonic. That is, the octaves, octave fifths and other harmonics are often sharp or flat of their theoretical frequencies. The particular harmonic series of each note of an instrument is what gives them their characteristic timbre. It's why a note on a piano doesn't sound like a note played on a trumpet, even if it's the "same" note.

Thus the heterodyning is much more hetero than has been thus far discussed.

This is a contradictory statement. Air is a gas which is like all gases compressible. Fluids are not compressible. If they were you could not brake with your car brakes. The effect of gas in your brake fluid is: Bad or no brakes.

ALL of my physics and aerodynamics profs taught otherwise.

Many laymen do confuse "fluid" with "liquid" though.

Quote

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

Although the term "fluid" includes both the liquid and gas phases, in common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present. For example, "brake fluid" is hydraulic oil and will not perform its required function if there is gas in it. This colloquial usage of the term is also common in medicine and in nutrition ("take plenty of fluids").[/url] --emphasis added

. . . A very good thing to pick up and give the young student is one of those small quartz tuners. For a Trumpet player, make sure that the Tuner is a Chromatic type and it is easier to use one that automatically changes pitches rather than one that is manually set to only one note at a time. This kind of visual feedback, if used for ten minutes a day for awhile in their regular practice regimen can really speed up the process that a Trumpet player must develop, which is the ability to hear the next tempered note in a scale in their head *before* attempting to play said note. . . .

I'm taking singing lessons (not an easy thing to start at age 67). I was bitching about my difficulty in staying "on pitch", and my teacher suggested a tuner. They're priced around $20, now.

I got one, and started using it. Came back to my lesson next week really discouraged -- the needle was wandering all over the scale, and I couldn't control it.

. . . "Yes", she said, "I cried for a while after I got mine."

It's a lot easier if you start in high school.<g>

. Charles

PS -- I know this is off-topic . . .

PPS -- the "beats" that a piano tuner hears -- or that anyone can hear, if two instruments are playing the same note _slightly_ out of tune -- are a _linear_ effect.

The Fourier analysis of the "two trumpets" tone shows two sine waves at slightly different frequencies.

If you graph the sound pressure level, you'll see a fast wave (at the played frequency) that _appears to be_ modulated by a slow wave (at the "difference frequency"). And your ear picks up that _apparent_ modulation, even though the Fourier analysis says it doesn't exist.

If you were to record the two trumpets, and play the signal back through a loudspeaker, you could put your finger on the speaker cone and _feel_ the signal go from "loud" to "nothing".

There's no "non-linearity" involved, but we _hear_ differently than we _analyze_.

This is a contradictory statement. Air is a gas which is like all gases compressible. Fluids are not compressible. If they were you could not brake with your car brakes. The effect of gas in your brake fluid is: Bad or no brakes.

Fluids and liquids are NOT the same thing. If it can flow, so as to fill a container of any given shape, it's a fluid (essentially the same etymology as "to flow".) Air is a fluid, as is water.

Sorry to complicate matters, but a single musical tone from a mechanical instrument or from an electronic instrument imitating a mechanical instrument is not a single frequency but rather a combination of frequencies beginning with a fundamental (harmonic) and then a complete harmonic series at octaves, octave fifths, octave thirds (sixths) and so forth. A further complication is that the harmonic series itself often is not precisely harmonic. That is, the octaves, octave fifths and other harmonics are often sharp or flat of their theoretical frequencies. The particular harmonic series of each note of an instrument is what gives them their characteristic timbre. It's why a note on a piano doesn't sound like a note played on a trumpet, even if it's the "same" note.

Thus the heterodyning is much more hetero than has been thus far discussed.

Good point. That's why the shape of the bell, and conical -vs- straight tubing make a huge difference in sound. Brass instruments all have subtle, but very different shapes to them that greatly affect the waveform generated.

Never thought I'd use that after the test! (I once was a music major, briefly).

When in the air force, going through tech school for Electronic Counter Measures, one of the things we did was take a couple of audio signal generators hooked up to speakers and set one to like 20,000 hz and the other at 23,000 hz and then remove the lamps that showed the power was on. we did this while the instructor was out of the room. the high pitched squeal was heard as a hetrodyne between the two generators and drove the guys nuts the first time, but after that they had out number.

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